Pensieve header: Notebook for Dalyell meeting 2: the Jones polynomial.

Find everything at http://drorbn.net/syd3

Print["Setting Knots to contain all from Knot[3,1] to Knot[10,165] as well as GST48..."];
Import["http://drorbn.net/AcademicPensieve/2016-09/GST48-Marked.png"]
Knots={Knot[3,1]->PD[X[1,4,2,5],X[3,6,4,1],X[5,2,6,3]],Knot[4,1]->PD[X[4,2,5,1],X[8,6,1,5],X[6,3,7,4],X[2,7,3,8]],Knot[5,1]->PD[X[1,6,2,7],X[3,8,4,9],X[5,10,6,1],X[7,2,8,3],X[9,4,10,5]],Knot[5,2]->PD[X[1,4,2,5],X[3,8,4,9],X[5,10,6,1],X[9,6,10,7],X[7,2,8,3]],Knot[6,1]->PD[X[1,4,2,5],X[7,10,8,11],X[3,9,4,8],X[9,3,10,2],X[5,12,6,1],X[11,6,12,7]],Knot[6,2]->PD[X[1,4,2,5],X[5,10,6,11],X[3,9,4,8],X[9,3,10,2],X[7,12,8,1],X[11,6,12,7]],Knot[6,3]->PD[X[4,2,5,1],X[8,4,9,3],X[12,9,1,10],X[10,5,11,6],X[6,11,7,12],X[2,8,3,7]],Knot[7,1]->PD[X[1,8,2,9],X[3,10,4,11],X[5,12,6,13],X[7,14,8,1],X[9,2,10,3],X[11,4,12,5],X[13,6,14,7]],Knot[7,2]->PD[X[1,4,2,5],X[3,10,4,11],X[5,14,6,1],X[7,12,8,13],X[11,8,12,9],X[13,6,14,7],X[9,2,10,3]],Knot[7,3]->PD[X[6,2,7,1],X[10,4,11,3],X[14,8,1,7],X[8,14,9,13],X[12,6,13,5],X[2,10,3,9],X[4,12,5,11]],Knot[7,4]->PD[X[6,2,7,1],X[12,6,13,5],X[14,8,1,7],X[8,14,9,13],X[2,12,3,11],X[10,4,11,3],X[4,10,5,9]],Knot[7,5]->PD[X[1,4,2,5],X[3,10,4,11],X[5,12,6,13],X[7,14,8,1],X[13,6,14,7],X[11,8,12,9],X[9,2,10,3]],Knot[7,6]->PD[X[1,4,2,5],X[3,8,4,9],X[5,12,6,13],X[9,1,10,14],X[13,11,14,10],X[11,6,12,7],X[7,2,8,3]],Knot[7,7]->PD[X[1,4,2,5],X[5,10,6,11],X[3,9,4,8],X[9,3,10,2],X[11,14,12,1],X[7,13,8,12],X[13,7,14,6]],Knot[8,1]->PD[X[1,4,2,5],X[9,12,10,13],X[3,11,4,10],X[11,3,12,2],X[5,16,6,1],X[7,14,8,15],X[13,8,14,9],X[15,6,16,7]],Knot[8,2]->PD[X[1,4,2,5],X[5,12,6,13],X[3,11,4,10],X[11,3,12,2],X[7,14,8,15],X[9,16,10,1],X[13,6,14,7],X[15,8,16,9]],Knot[8,3]->PD[X[6,2,7,1],X[14,10,15,9],X[10,5,11,6],X[12,3,13,4],X[4,11,5,12],X[2,13,3,14],X[16,8,1,7],X[8,16,9,15]],Knot[8,4]->PD[X[6,2,7,1],X[14,10,15,9],X[10,3,11,4],X[2,13,3,14],X[12,5,13,6],X[16,8,1,7],X[4,11,5,12],X[8,16,9,15]],Knot[8,5]->PD[X[6,2,7,1],X[8,4,9,3],X[2,8,3,7],X[14,10,15,9],X[12,5,13,6],X[4,13,5,14],X[16,12,1,11],X[10,16,11,15]],Knot[8,6]->PD[X[1,4,2,5],X[9,12,10,13],X[3,11,4,10],X[11,3,12,2],X[5,14,6,15],X[7,16,8,1],X[15,6,16,7],X[13,8,14,9]],Knot[8,7]->PD[X[1,4,2,5],X[3,10,4,11],X[11,1,12,16],X[5,13,6,12],X[7,15,8,14],X[13,7,14,6],X[15,9,16,8],X[9,2,10,3]],Knot[8,8]->PD[X[1,4,2,5],X[3,8,4,9],X[11,15,12,14],X[5,13,6,12],X[13,7,14,6],X[9,1,10,16],X[15,11,16,10],X[7,2,8,3]],Knot[8,9]->PD[X[6,2,7,1],X[14,8,15,7],X[10,3,11,4],X[2,13,3,14],X[12,5,13,6],X[4,11,5,12],X[16,10,1,9],X[8,16,9,15]],Knot[8,10]->PD[X[1,4,2,5],X[3,8,4,9],X[9,15,10,14],X[5,13,6,12],X[13,7,14,6],X[11,1,12,16],X[15,11,16,10],X[7,2,8,3]],Knot[8,11]->PD[X[1,4,2,5],X[5,12,6,13],X[3,11,4,10],X[11,3,12,2],X[9,16,10,1],X[15,6,16,7],X[7,14,8,15],X[13,8,14,9]],Knot[8,12]->PD[X[4,2,5,1],X[10,8,11,7],X[8,3,9,4],X[2,9,3,10],X[14,6,15,5],X[16,11,1,12],X[12,15,13,16],X[6,14,7,13]],Knot[8,13]->PD[X[1,4,2,5],X[3,10,4,11],X[11,1,12,16],X[5,13,6,12],X[15,7,16,6],X[7,15,8,14],X[13,9,14,8],X[9,2,10,3]],Knot[8,14]->PD[X[1,4,2,5],X[5,10,6,11],X[3,9,4,8],X[9,3,10,2],X[7,14,8,15],X[11,16,12,1],X[15,12,16,13],X[13,6,14,7]],Knot[8,15]->PD[X[1,4,2,5],X[3,8,4,9],X[5,12,6,13],X[13,16,14,1],X[9,14,10,15],X[15,10,16,11],X[11,6,12,7],X[7,2,8,3]],Knot[8,16]->PD[X[6,2,7,1],X[14,6,15,5],X[16,11,1,12],X[12,7,13,8],X[8,3,9,4],X[4,9,5,10],X[10,15,11,16],X[2,14,3,13]],Knot[8,17]->PD[X[6,2,7,1],X[14,8,15,7],X[8,3,9,4],X[2,13,3,14],X[12,5,13,6],X[4,9,5,10],X[16,12,1,11],X[10,16,11,15]],Knot[8,18]->PD[X[6,2,7,1],X[8,3,9,4],X[16,11,1,12],X[2,14,3,13],X[4,15,5,16],X[10,6,11,5],X[12,7,13,8],X[14,10,15,9]],Knot[8,19]->PD[X[4,2,5,1],X[8,4,9,3],X[9,15,10,14],X[5,13,6,12],X[13,7,14,6],X[11,1,12,16],X[15,11,16,10],X[2,8,3,7]],Knot[8,20]->PD[X[4,2,5,1],X[8,4,9,3],X[5,12,6,13],X[13,16,14,1],X[9,14,10,15],X[15,10,16,11],X[11,6,12,7],X[2,8,3,7]],Knot[8,21]->PD[X[1,4,2,5],X[3,8,4,9],X[12,6,13,5],X[13,16,14,1],X[9,14,10,15],X[15,10,16,11],X[6,12,7,11],X[7,2,8,3]],Knot[9,1]->PD[X[1,10,2,11],X[3,12,4,13],X[5,14,6,15],X[7,16,8,17],X[9,18,10,1],X[11,2,12,3],X[13,4,14,5],X[15,6,16,7],X[17,8,18,9]],Knot[9,2]->PD[X[1,4,2,5],X[3,12,4,13],X[5,18,6,1],X[7,16,8,17],X[9,14,10,15],X[13,10,14,11],X[15,8,16,9],X[17,6,18,7],X[11,2,12,3]],Knot[9,3]->PD[X[8,2,9,1],X[12,4,13,3],X[18,10,1,9],X[10,18,11,17],X[14,6,15,5],X[16,8,17,7],X[2,12,3,11],X[4,14,5,13],X[6,16,7,15]],Knot[9,4]->PD[X[1,6,2,7],X[3,12,4,13],X[7,18,8,1],X[9,16,10,17],X[15,10,16,11],X[17,8,18,9],X[5,14,6,15],X[11,2,12,3],X[13,4,14,5]],Knot[9,5]->PD[X[6,2,7,1],X[14,6,15,5],X[18,8,1,7],X[16,10,17,9],X[10,16,11,15],X[8,18,9,17],X[2,14,3,13],X[12,4,13,3],X[4,12,5,11]],Knot[9,6]->PD[X[1,4,2,5],X[3,12,4,13],X[5,14,6,15],X[7,16,8,17],X[9,18,10,1],X[15,6,16,7],X[17,8,18,9],X[13,10,14,11],X[11,2,12,3]],Knot[9,7]->PD[X[1,4,2,5],X[3,12,4,13],X[5,16,6,17],X[7,18,8,1],X[17,6,18,7],X[9,14,10,15],X[13,10,14,11],X[15,8,16,9],X[11,2,12,3]],Knot[9,8]->PD[X[1,4,2,5],X[3,8,4,9],X[5,14,6,15],X[9,1,10,18],X[11,17,12,16],X[15,13,16,12],X[17,11,18,10],X[13,6,14,7],X[7,2,8,3]],Knot[9,9]->PD[X[1,6,2,7],X[3,12,4,13],X[7,16,8,17],X[9,18,10,1],X[17,8,18,9],X[15,10,16,11],X[5,14,6,15],X[11,2,12,3],X[13,4,14,5]],Knot[9,10]->PD[X[8,2,9,1],X[12,4,13,3],X[18,10,1,9],X[10,18,11,17],X[16,8,17,7],X[2,12,3,11],X[4,16,5,15],X[14,6,15,5],X[6,14,7,13]],Knot[9,11]->PD[X[1,4,2,5],X[9,12,10,13],X[3,11,4,10],X[11,3,12,2],X[13,1,14,18],X[5,15,6,14],X[7,17,8,16],X[15,7,16,6],X[17,9,18,8]],Knot[9,12]->PD[X[1,4,2,5],X[3,10,4,11],X[5,16,6,17],X[11,1,12,18],X[17,13,18,12],X[7,14,8,15],X[13,8,14,9],X[15,6,16,7],X[9,2,10,3]],Knot[9,13]->PD[X[6,2,7,1],X[14,6,15,5],X[16,8,17,7],X[18,10,1,9],X[8,18,9,17],X[10,16,11,15],X[2,14,3,13],X[12,4,13,3],X[4,12,5,11]],Knot[9,14]->PD[X[1,4,2,5],X[5,12,6,13],X[3,11,4,10],X[11,3,12,2],X[13,18,14,1],X[9,15,10,14],X[7,17,8,16],X[15,9,16,8],X[17,7,18,6]],Knot[9,15]->PD[X[1,4,2,5],X[7,10,8,11],X[3,9,4,8],X[9,3,10,2],X[13,17,14,16],X[5,15,6,14],X[15,7,16,6],X[11,1,12,18],X[17,13,18,12]],Knot[9,16]->PD[X[4,2,5,1],X[12,4,13,3],X[16,6,17,5],X[18,8,1,7],X[6,18,7,17],X[10,16,11,15],X[14,10,15,9],X[8,14,9,13],X[2,12,3,11]],Knot[9,17]->PD[X[1,4,2,5],X[5,12,6,13],X[3,11,4,10],X[11,3,12,2],X[7,14,8,15],X[13,6,14,7],X[15,18,16,1],X[9,17,10,16],X[17,9,18,8]],Knot[9,18]->PD[X[1,4,2,5],X[3,12,4,13],X[5,14,6,15],X[9,18,10,1],X[17,6,18,7],X[7,16,8,17],X[15,8,16,9],X[13,10,14,11],X[11,2,12,3]],Knot[9,19]->PD[X[1,4,2,5],X[5,10,6,11],X[3,9,4,8],X[9,3,10,2],X[13,16,14,17],X[7,15,8,14],X[15,7,16,6],X[11,18,12,1],X[17,12,18,13]],Knot[9,20]->PD[X[1,4,2,5],X[3,10,4,11],X[5,14,6,15],X[7,16,8,17],X[11,1,12,18],X[15,6,16,7],X[17,13,18,12],X[13,8,14,9],X[9,2,10,3]],Knot[9,21]->PD[X[1,4,2,5],X[9,12,10,13],X[3,11,4,10],X[11,3,12,2],X[13,1,14,18],X[5,15,6,14],X[17,7,18,6],X[7,17,8,16],X[15,9,16,8]],Knot[9,22]->PD[X[4,2,5,1],X[10,6,11,5],X[8,3,9,4],X[2,9,3,10],X[16,12,17,11],X[14,7,15,8],X[6,15,7,16],X[18,14,1,13],X[12,18,13,17]],Knot[9,23]->PD[X[1,4,2,5],X[3,10,4,11],X[5,12,6,13],X[7,16,8,17],X[13,18,14,1],X[17,14,18,15],X[15,6,16,7],X[11,8,12,9],X[9,2,10,3]],Knot[9,24]->PD[X[1,4,2,5],X[3,8,4,9],X[5,14,6,15],X[9,17,10,16],X[11,1,12,18],X[17,11,18,10],X[15,13,16,12],X[13,6,14,7],X[7,2,8,3]],Knot[9,25]->PD[X[1,4,2,5],X[3,8,4,9],X[5,12,6,13],X[9,17,10,16],X[13,18,14,1],X[17,14,18,15],X[15,11,16,10],X[11,6,12,7],X[7,2,8,3]],Knot[9,26]->PD[X[1,4,2,5],X[5,12,6,13],X[3,11,4,10],X[11,3,12,2],X[13,18,14,1],X[7,15,8,14],X[17,7,18,6],X[9,17,10,16],X[15,9,16,8]],Knot[9,27]->PD[X[1,4,2,5],X[3,10,4,11],X[11,1,12,18],X[5,13,6,12],X[13,17,14,16],X[7,14,8,15],X[15,6,16,7],X[17,9,18,8],X[9,2,10,3]],Knot[9,28]->PD[X[1,4,2,5],X[3,8,4,9],X[11,15,12,14],X[5,13,6,12],X[13,7,14,6],X[15,18,16,1],X[9,16,10,17],X[17,10,18,11],X[7,2,8,3]],Knot[9,29]->PD[X[6,2,7,1],X[16,11,17,12],X[10,4,11,3],X[2,15,3,16],X[14,5,15,6],X[18,8,1,7],X[4,10,5,9],X[12,17,13,18],X[8,13,9,14]],Knot[9,30]->PD[X[4,2,5,1],X[10,6,11,5],X[8,3,9,4],X[2,9,3,10],X[14,8,15,7],X[18,15,1,16],X[16,11,17,12],X[12,17,13,18],X[6,14,7,13]],Knot[9,31]->PD[X[1,4,2,5],X[3,10,4,11],X[11,1,12,18],X[5,13,6,12],X[17,7,18,6],X[7,14,8,15],X[13,16,14,17],X[15,8,16,9],X[9,2,10,3]],Knot[9,32]->PD[X[1,4,2,5],X[13,18,14,1],X[3,9,4,8],X[9,3,10,2],X[7,15,8,14],X[15,11,16,10],X[5,12,6,13],X[11,17,12,16],X[17,7,18,6]],Knot[9,33]->PD[X[4,2,5,1],X[12,8,13,7],X[8,3,9,4],X[2,9,3,10],X[18,13,1,14],X[14,5,15,6],X[6,17,7,18],X[16,12,17,11],X[10,16,11,15]],Knot[9,34]->PD[X[6,2,7,1],X[16,8,17,7],X[8,3,9,4],X[2,15,3,16],X[14,9,15,10],X[10,6,11,5],X[4,14,5,13],X[18,11,1,12],X[12,17,13,18]],Knot[9,35]->PD[X[1,8,2,9],X[7,14,8,15],X[5,16,6,17],X[9,18,10,1],X[15,6,16,7],X[17,10,18,11],X[13,2,14,3],X[3,12,4,13],X[11,4,12,5]],Knot[9,36]->PD[X[1,4,2,5],X[7,10,8,11],X[3,9,4,8],X[9,3,10,2],X[11,17,12,16],X[5,15,6,14],X[15,7,16,6],X[13,1,14,18],X[17,13,18,12]],Knot[9,37]->PD[X[1,4,2,5],X[7,12,8,13],X[3,11,4,10],X[11,3,12,2],X[5,14,6,15],X[13,6,14,7],X[15,18,16,1],X[9,17,10,16],X[17,9,18,8]],Knot[9,38]->PD[X[1,6,2,7],X[5,14,6,15],X[7,18,8,1],X[15,8,16,9],X[3,10,4,11],X[9,4,10,5],X[17,12,18,13],X[11,16,12,17],X[13,2,14,3]],Knot[9,39]->PD[X[1,6,2,7],X[3,11,4,10],X[7,18,8,1],X[17,13,18,12],X[9,17,10,16],X[5,15,6,14],X[15,5,16,4],X[11,3,12,2],X[13,9,14,8]],Knot[9,40]->PD[X[1,6,2,7],X[7,12,8,13],X[5,15,6,14],X[11,3,12,2],X[15,10,16,11],X[3,16,4,17],X[9,4,10,5],X[17,9,18,8],X[13,18,14,1]],Knot[9,41]->PD[X[6,2,7,1],X[12,8,13,7],X[14,5,15,6],X[10,3,11,4],X[2,11,3,12],X[4,15,5,16],X[8,17,9,18],X[16,9,17,10],X[18,14,1,13]],Knot[9,42]->PD[X[1,4,2,5],X[5,10,6,11],X[3,9,4,8],X[9,3,10,2],X[16,12,17,11],X[14,7,15,8],X[6,15,7,16],X[18,14,1,13],X[12,18,13,17]],Knot[9,43]->PD[X[4,2,5,1],X[10,6,11,5],X[8,3,9,4],X[2,9,3,10],X[14,8,15,7],X[15,1,16,18],X[11,17,12,16],X[17,13,18,12],X[6,14,7,13]],Knot[9,44]->PD[X[1,4,2,5],X[5,10,6,11],X[3,9,4,8],X[9,3,10,2],X[14,8,15,7],X[18,15,1,16],X[16,11,17,12],X[12,17,13,18],X[6,14,7,13]],Knot[9,45]->PD[X[4,2,5,1],X[10,6,11,5],X[8,3,9,4],X[2,9,3,10],X[7,14,8,15],X[18,15,1,16],X[16,11,17,12],X[12,17,13,18],X[13,6,14,7]],Knot[9,46]->PD[X[4,2,5,1],X[7,12,8,13],X[10,3,11,4],X[2,11,3,12],X[5,14,6,15],X[13,6,14,7],X[15,18,16,1],X[9,17,10,16],X[17,9,18,8]],Knot[9,47]->PD[X[6,2,7,1],X[16,8,17,7],X[8,3,9,4],X[2,15,3,16],X[14,9,15,10],X[10,6,11,5],X[4,14,5,13],X[11,1,12,18],X[17,13,18,12]],Knot[9,48]->PD[X[1,4,2,5],X[12,8,13,7],X[3,11,4,10],X[11,3,12,2],X[14,6,15,5],X[6,14,7,13],X[15,18,16,1],X[9,17,10,16],X[17,9,18,8]],Knot[9,49]->PD[X[6,2,7,1],X[12,8,13,7],X[5,15,6,14],X[3,11,4,10],X[11,3,12,2],X[15,5,16,4],X[17,9,18,8],X[9,17,10,16],X[18,14,1,13]],Knot[10,1]->PD[X[1,4,2,5],X[11,14,12,15],X[3,13,4,12],X[13,3,14,2],X[5,20,6,1],X[7,18,8,19],X[9,16,10,17],X[15,10,16,11],X[17,8,18,9],X[19,6,20,7]],Knot[10,2]->PD[X[1,4,2,5],X[5,14,6,15],X[3,13,4,12],X[13,3,14,2],X[7,16,8,17],X[9,18,10,19],X[11,20,12,1],X[15,6,16,7],X[17,8,18,9],X[19,10,20,11]],Knot[10,3]->PD[X[1,6,2,7],X[11,16,12,17],X[5,13,6,12],X[3,15,4,14],X[13,5,14,4],X[15,3,16,2],X[7,20,8,1],X[9,18,10,19],X[17,10,18,11],X[19,8,20,9]],Knot[10,4]->PD[X[6,2,7,1],X[16,12,17,11],X[12,3,13,4],X[2,15,3,16],X[14,5,15,6],X[20,8,1,7],X[18,10,19,9],X[4,13,5,14],X[10,18,11,17],X[8,20,9,19]],Knot[10,5]->PD[X[1,4,2,5],X[3,12,4,13],X[13,1,14,20],X[5,15,6,14],X[7,17,8,16],X[9,19,10,18],X[15,7,16,6],X[17,9,18,8],X[19,11,20,10],X[11,2,12,3]],Knot[10,6]->PD[X[1,4,2,5],X[11,14,12,15],X[3,13,4,12],X[13,3,14,2],X[5,16,6,17],X[7,18,8,19],X[9,20,10,1],X[17,6,18,7],X[19,8,20,9],X[15,10,16,11]],Knot[10,7]->PD[X[1,4,2,5],X[5,14,6,15],X[3,13,4,12],X[13,3,14,2],X[11,20,12,1],X[19,6,20,7],X[7,18,8,19],X[9,16,10,17],X[15,10,16,11],X[17,8,18,9]],Knot[10,8]->PD[X[1,6,2,7],X[7,16,8,17],X[5,13,6,12],X[3,15,4,14],X[13,5,14,4],X[15,3,16,2],X[9,18,10,19],X[11,20,12,1],X[17,8,18,9],X[19,10,20,11]],Knot[10,9]->PD[X[6,2,7,1],X[16,8,17,7],X[12,3,13,4],X[2,15,3,16],X[14,5,15,6],X[4,13,5,14],X[18,10,19,9],X[20,12,1,11],X[8,18,9,17],X[10,20,11,19]],Knot[10,10]->PD[X[1,4,2,5],X[3,12,4,13],X[13,1,14,20],X[5,15,6,14],X[19,7,20,6],X[7,19,8,18],X[9,17,10,16],X[15,11,16,10],X[17,9,18,8],X[11,2,12,3]],Knot[10,11]->PD[X[1,6,2,7],X[11,16,12,17],X[5,13,6,12],X[3,15,4,14],X[13,5,14,4],X[15,3,16,2],X[7,18,8,19],X[9,20,10,1],X[19,8,20,9],X[17,10,18,11]],Knot[10,12]->PD[X[1,4,2,5],X[3,10,4,11],X[13,19,14,18],X[5,15,6,14],X[7,17,8,16],X[15,7,16,6],X[17,9,18,8],X[11,1,12,20],X[19,13,20,12],X[9,2,10,3]],Knot[10,13]->PD[X[1,4,2,5],X[9,12,10,13],X[3,11,4,10],X[11,3,12,2],X[5,18,6,19],X[13,1,14,20],X[19,15,20,14],X[7,16,8,17],X[15,8,16,9],X[17,6,18,7]],Knot[10,14]->PD[X[1,4,2,5],X[5,12,6,13],X[3,11,4,10],X[11,3,12,2],X[7,16,8,17],X[13,20,14,1],X[19,14,20,15],X[9,18,10,19],X[15,6,16,7],X[17,8,18,9]],Knot[10,15]->PD[X[1,4,2,5],X[3,12,4,13],X[9,14,10,15],X[13,10,14,11],X[15,1,16,20],X[5,17,6,16],X[7,19,8,18],X[17,7,18,6],X[19,9,20,8],X[11,2,12,3]],Knot[10,16]->PD[X[6,2,7,1],X[16,8,17,7],X[12,5,13,6],X[14,3,15,4],X[4,13,5,14],X[2,15,3,16],X[20,12,1,11],X[8,20,9,19],X[18,10,19,9],X[10,18,11,17]],Knot[10,17]->PD[X[6,2,7,1],X[12,4,13,3],X[20,15,1,16],X[16,7,17,8],X[18,9,19,10],X[8,17,9,18],X[10,19,11,20],X[14,6,15,5],X[2,12,3,11],X[4,14,5,13]],Knot[10,18]->PD[X[1,4,2,5],X[3,12,4,13],X[5,14,6,15],X[15,20,16,1],X[9,17,10,16],X[7,19,8,18],X[17,9,18,8],X[19,7,20,6],X[13,10,14,11],X[11,2,12,3]],Knot[10,19]->PD[X[1,6,2,7],X[3,12,4,13],X[15,1,16,20],X[7,17,8,16],X[19,9,20,8],X[9,19,10,18],X[17,11,18,10],X[5,14,6,15],X[11,2,12,3],X[13,4,14,5]],Knot[10,20]->PD[X[1,4,2,5],X[11,14,12,15],X[3,13,4,12],X[13,3,14,2],X[5,18,6,19],X[7,20,8,1],X[19,6,20,7],X[9,16,10,17],X[15,10,16,11],X[17,8,18,9]],Knot[10,21]->PD[X[1,4,2,5],X[5,14,6,15],X[3,13,4,12],X[13,3,14,2],X[7,16,8,17],X[11,20,12,1],X[15,6,16,7],X[19,8,20,9],X[9,18,10,19],X[17,10,18,11]],Knot[10,22]->PD[X[6,2,7,1],X[16,12,17,11],X[12,3,13,4],X[2,15,3,16],X[14,5,15,6],X[18,8,19,7],X[20,10,1,9],X[8,20,9,19],X[4,13,5,14],X[10,18,11,17]],Knot[10,23]->PD[X[1,4,2,5],X[3,12,4,13],X[13,1,14,20],X[5,15,6,14],X[7,17,8,16],X[15,7,16,6],X[19,9,20,8],X[9,19,10,18],X[17,11,18,10],X[11,2,12,3]],Knot[10,24]->PD[X[1,4,2,5],X[11,14,12,15],X[3,13,4,12],X[13,3,14,2],X[5,16,6,17],X[9,20,10,1],X[19,6,20,7],X[7,18,8,19],X[17,8,18,9],X[15,10,16,11]],Knot[10,25]->PD[X[1,4,2,5],X[5,14,6,15],X[3,13,4,12],X[13,3,14,2],X[11,20,12,1],X[19,6,20,7],X[9,18,10,19],X[7,16,8,17],X[17,8,18,9],X[15,10,16,11]],Knot[10,26]->PD[X[6,2,7,1],X[16,8,17,7],X[12,3,13,4],X[2,15,3,16],X[14,5,15,6],X[4,13,5,14],X[20,12,1,11],X[8,20,9,19],X[18,10,19,9],X[10,18,11,17]],Knot[10,27]->PD[X[4,2,5,1],X[12,4,13,3],X[20,13,1,14],X[14,5,15,6],X[6,19,7,20],X[18,9,19,10],X[16,7,17,8],X[8,17,9,18],X[10,15,11,16],X[2,12,3,11]],Knot[10,28]->PD[X[1,4,2,5],X[3,10,4,11],X[13,19,14,18],X[5,15,6,14],X[17,7,18,6],X[7,17,8,16],X[15,9,16,8],X[11,1,12,20],X[19,13,20,12],X[9,2,10,3]],Knot[10,29]->PD[X[1,4,2,5],X[9,12,10,13],X[3,11,4,10],X[11,3,12,2],X[5,16,6,17],X[7,18,8,19],X[13,1,14,20],X[17,6,18,7],X[19,15,20,14],X[15,8,16,9]],Knot[10,30]->PD[X[1,4,2,5],X[5,12,6,13],X[3,11,4,10],X[11,3,12,2],X[9,18,10,19],X[13,20,14,1],X[19,14,20,15],X[17,6,18,7],X[7,16,8,17],X[15,8,16,9]],Knot[10,31]->PD[X[1,4,2,5],X[3,12,4,13],X[9,14,10,15],X[13,10,14,11],X[15,1,16,20],X[5,17,6,16],X[19,7,20,6],X[7,19,8,18],X[17,9,18,8],X[11,2,12,3]],Knot[10,32]->PD[X[1,4,2,5],X[3,12,4,13],X[5,14,6,15],X[15,20,16,1],X[7,17,8,16],X[19,7,20,6],X[9,19,10,18],X[17,9,18,8],X[13,10,14,11],X[11,2,12,3]],Knot[10,33]->PD[X[6,2,7,1],X[14,6,15,5],X[20,15,1,16],X[16,7,17,8],X[8,19,9,20],X[18,9,19,10],X[10,17,11,18],X[2,14,3,13],X[12,4,13,3],X[4,12,5,11]],Knot[10,34]->PD[X[1,4,2,5],X[3,8,4,9],X[13,17,14,16],X[5,15,6,14],X[15,7,16,6],X[9,1,10,20],X[11,19,12,18],X[17,13,18,12],X[19,11,20,10],X[7,2,8,3]],Knot[10,35]->PD[X[1,4,2,5],X[7,10,8,11],X[3,9,4,8],X[9,3,10,2],X[5,16,6,17],X[11,1,12,20],X[13,19,14,18],X[17,15,18,14],X[19,13,20,12],X[15,6,16,7]],Knot[10,36]->PD[X[1,4,2,5],X[5,10,6,11],X[3,9,4,8],X[9,3,10,2],X[7,16,8,17],X[11,20,12,1],X[13,18,14,19],X[17,14,18,15],X[19,12,20,13],X[15,6,16,7]],Knot[10,37]->PD[X[4,2,5,1],X[10,4,11,3],X[12,8,13,7],X[8,12,9,11],X[18,15,19,16],X[16,5,17,6],X[6,17,7,18],X[20,13,1,14],X[14,19,15,20],X[2,10,3,9]],Knot[10,38]->PD[X[1,4,2,5],X[3,10,4,11],X[5,12,6,13],X[15,18,16,19],X[7,17,8,16],X[17,7,18,6],X[13,20,14,1],X[19,14,20,15],X[11,8,12,9],X[9,2,10,3]],Knot[10,39]->PD[X[1,4,2,5],X[5,12,6,13],X[3,11,4,10],X[11,3,12,2],X[7,14,8,15],X[9,18,10,19],X[15,20,16,1],X[19,16,20,17],X[13,6,14,7],X[17,8,18,9]],Knot[10,40]->PD[X[1,4,2,5],X[3,10,4,11],X[11,1,12,20],X[5,13,6,12],X[7,17,8,16],X[15,19,16,18],X[19,15,20,14],X[13,7,14,6],X[17,9,18,8],X[9,2,10,3]],Knot[10,41]->PD[X[1,4,2,5],X[5,12,6,13],X[3,11,4,10],X[11,3,12,2],X[9,20,10,1],X[15,19,16,18],X[13,8,14,9],X[17,6,18,7],X[7,16,8,17],X[19,15,20,14]],Knot[10,42]->PD[X[1,4,2,5],X[3,10,4,11],X[11,1,12,20],X[5,13,6,12],X[15,18,16,19],X[13,9,14,8],X[17,7,18,6],X[7,17,8,16],X[19,14,20,15],X[9,2,10,3]],Knot[10,43]->PD[X[4,2,5,1],X[10,4,11,3],X[14,8,15,7],X[20,11,1,12],X[12,19,13,20],X[8,14,9,13],X[18,15,19,16],X[16,5,17,6],X[6,17,7,18],X[2,10,3,9]],Knot[10,44]->PD[X[1,4,2,5],X[5,12,6,13],X[3,11,4,10],X[11,3,12,2],X[13,20,14,1],X[9,15,10,14],X[15,18,16,19],X[7,16,8,17],X[17,8,18,9],X[19,7,20,6]],Knot[10,45]->PD[X[4,2,5,1],X[12,6,13,5],X[10,3,11,4],X[2,11,3,12],X[20,14,1,13],X[14,7,15,8],X[6,19,7,20],X[18,15,19,16],X[16,10,17,9],X[8,18,9,17]],Knot[10,46]->PD[X[6,2,7,1],X[8,4,9,3],X[2,8,3,7],X[16,10,17,9],X[14,5,15,6],X[4,15,5,16],X[18,12,19,11],X[20,14,1,13],X[10,18,11,17],X[12,20,13,19]],Knot[10,47]->PD[X[1,4,2,5],X[3,8,4,9],X[9,17,10,16],X[5,15,6,14],X[15,7,16,6],X[11,19,12,18],X[13,1,14,20],X[17,11,18,10],X[19,13,20,12],X[7,2,8,3]],Knot[10,48]->PD[X[6,2,7,1],X[8,4,9,3],X[14,6,15,5],X[20,15,1,16],X[16,9,17,10],X[18,11,19,12],X[10,17,11,18],X[12,19,13,20],X[2,8,3,7],X[4,14,5,13]],Knot[10,49]->PD[X[1,4,2,5],X[3,8,4,9],X[5,14,6,15],X[15,20,16,1],X[9,16,10,17],X[11,18,12,19],X[17,10,18,11],X[19,12,20,13],X[13,6,14,7],X[7,2,8,3]],Knot[10,50]->PD[X[6,2,7,1],X[8,4,9,3],X[2,8,3,7],X[16,10,17,9],X[14,5,15,6],X[4,15,5,16],X[20,14,1,13],X[10,20,11,19],X[18,12,19,11],X[12,18,13,17]],Knot[10,51]->PD[X[1,4,2,5],X[3,8,4,9],X[9,17,10,16],X[5,15,6,14],X[15,7,16,6],X[13,1,14,20],X[19,11,20,10],X[11,19,12,18],X[17,13,18,12],X[7,2,8,3]],Knot[10,52]->PD[X[6,2,7,1],X[8,4,9,3],X[14,6,15,5],X[20,15,1,16],X[16,9,17,10],X[10,19,11,20],X[18,11,19,12],X[12,17,13,18],X[2,8,3,7],X[4,14,5,13]],Knot[10,53]->PD[X[1,4,2,5],X[3,8,4,9],X[5,14,6,15],X[15,20,16,1],X[9,16,10,17],X[19,10,20,11],X[11,18,12,19],X[17,12,18,13],X[13,6,14,7],X[7,2,8,3]],Knot[10,54]->PD[X[1,4,2,5],X[3,10,4,11],X[7,12,8,13],X[11,8,12,9],X[13,19,14,18],X[5,17,6,16],X[17,7,18,6],X[15,1,16,20],X[19,15,20,14],X[9,2,10,3]],Knot[10,55]->PD[X[1,4,2,5],X[3,8,4,9],X[5,12,6,13],X[15,18,16,19],X[9,16,10,17],X[17,10,18,11],X[13,20,14,1],X[19,14,20,15],X[11,6,12,7],X[7,2,8,3]],Knot[10,56]->PD[X[4,2,5,1],X[10,4,11,3],X[12,6,13,5],X[18,14,19,13],X[16,7,17,8],X[6,17,7,18],X[20,16,1,15],X[14,20,15,19],X[8,12,9,11],X[2,10,3,9]],Knot[10,57]->PD[X[1,4,2,5],X[3,8,4,9],X[9,15,10,14],X[5,13,6,12],X[13,7,14,6],X[11,19,12,18],X[15,1,16,20],X[19,17,20,16],X[17,11,18,10],X[7,2,8,3]],Knot[10,58]->PD[X[1,4,2,5],X[7,10,8,11],X[3,9,4,8],X[9,3,10,2],X[5,14,6,15],X[11,19,12,18],X[15,20,16,1],X[19,16,20,17],X[17,13,18,12],X[13,6,14,7]],Knot[10,59]->PD[X[4,2,5,1],X[10,6,11,5],X[8,3,9,4],X[2,9,3,10],X[14,8,15,7],X[18,12,19,11],X[20,15,1,16],X[16,19,17,20],X[12,18,13,17],X[6,14,7,13]],Knot[10,60]->PD[X[4,2,5,1],X[10,6,11,5],X[8,3,9,4],X[2,9,3,10],X[16,12,17,11],X[14,7,15,8],X[6,15,7,16],X[20,18,1,17],X[18,13,19,14],X[12,19,13,20]],Knot[10,61]->PD[X[8,2,9,1],X[10,4,11,3],X[2,10,3,9],X[18,12,19,11],X[14,7,15,8],X[16,5,17,6],X[6,15,7,16],X[4,17,5,18],X[20,14,1,13],X[12,20,13,19]],Knot[10,62]->PD[X[1,4,2,5],X[3,10,4,11],X[11,19,12,18],X[5,15,6,14],X[7,17,8,16],X[15,7,16,6],X[17,9,18,8],X[13,1,14,20],X[19,13,20,12],X[9,2,10,3]],Knot[10,63]->PD[X[1,4,2,5],X[3,10,4,11],X[5,16,6,17],X[17,20,18,1],X[11,18,12,19],X[19,12,20,13],X[7,14,8,15],X[13,8,14,9],X[15,6,16,7],X[9,2,10,3]],Knot[10,64]->PD[X[8,2,9,1],X[10,4,11,3],X[2,10,3,9],X[18,12,19,11],X[14,5,15,6],X[4,17,5,18],X[16,7,17,8],X[6,15,7,16],X[20,14,1,13],X[12,20,13,19]],Knot[10,65]->PD[X[1,4,2,5],X[3,10,4,11],X[11,19,12,18],X[5,15,6,14],X[17,7,18,6],X[7,17,8,16],X[15,9,16,8],X[13,1,14,20],X[19,13,20,12],X[9,2,10,3]],Knot[10,66]->PD[X[1,4,2,5],X[3,10,4,11],X[5,14,6,15],X[7,16,8,17],X[15,6,16,7],X[17,20,18,1],X[11,18,12,19],X[19,12,20,13],X[13,8,14,9],X[9,2,10,3]],Knot[10,67]->PD[X[1,4,2,5],X[7,12,8,13],X[3,11,4,10],X[11,3,12,2],X[5,14,6,15],X[13,6,14,7],X[9,18,10,19],X[15,20,16,1],X[19,16,20,17],X[17,8,18,9]],Knot[10,68]->PD[X[4,2,5,1],X[12,4,13,3],X[20,13,1,14],X[16,5,17,6],X[8,19,9,20],X[18,9,19,10],X[10,17,11,18],X[14,7,15,8],X[6,15,7,16],X[2,12,3,11]],Knot[10,69]->PD[X[1,4,2,5],X[7,12,8,13],X[3,11,4,10],X[11,3,12,2],X[13,17,14,16],X[5,15,6,14],X[15,7,16,6],X[17,20,18,1],X[9,19,10,18],X[19,9,20,8]],Knot[10,70]->PD[X[1,4,2,5],X[7,10,8,11],X[3,9,4,8],X[9,3,10,2],X[5,16,6,17],X[11,19,12,18],X[13,1,14,20],X[19,13,20,12],X[17,15,18,14],X[15,6,16,7]],Knot[10,71]->PD[X[1,4,2,5],X[3,8,4,9],X[11,15,12,14],X[5,13,6,12],X[13,7,14,6],X[9,19,10,18],X[15,20,16,1],X[19,16,20,17],X[17,11,18,10],X[7,2,8,3]],Knot[10,72]->PD[X[4,2,5,1],X[10,6,11,5],X[8,3,9,4],X[2,9,3,10],X[16,8,17,7],X[18,12,19,11],X[20,14,1,13],X[12,20,13,19],X[14,18,15,17],X[6,16,7,15]],Knot[10,73]->PD[X[4,2,5,1],X[10,6,11,5],X[8,3,9,4],X[2,9,3,10],X[16,14,17,13],X[14,7,15,8],X[6,15,7,16],X[20,17,1,18],X[18,11,19,12],X[12,19,13,20]],Knot[10,74]->PD[X[1,4,2,5],X[5,14,6,15],X[3,13,4,12],X[13,3,14,2],X[11,18,12,19],X[9,20,10,1],X[19,10,20,11],X[17,6,18,7],X[7,16,8,17],X[15,8,16,9]],Knot[10,75]->PD[X[1,4,2,5],X[5,12,6,13],X[3,11,4,10],X[11,3,12,2],X[13,16,14,17],X[7,15,8,14],X[15,7,16,6],X[17,20,18,1],X[9,19,10,18],X[19,9,20,8]],Knot[10,76]->PD[X[4,2,5,1],X[14,10,15,9],X[12,3,13,4],X[2,13,3,14],X[18,6,19,5],X[20,8,1,7],X[6,20,7,19],X[8,18,9,17],X[16,12,17,11],X[10,16,11,15]],Knot[10,77]->PD[X[1,4,2,5],X[3,8,4,9],X[13,17,14,16],X[5,15,6,14],X[15,7,16,6],X[9,19,10,18],X[11,1,12,20],X[19,11,20,10],X[17,13,18,12],X[7,2,8,3]],Knot[10,78]->PD[X[1,4,2,5],X[3,8,4,9],X[5,14,6,15],X[11,17,12,16],X[15,13,16,12],X[17,20,18,1],X[9,18,10,19],X[19,10,20,11],X[13,6,14,7],X[7,2,8,3]],Knot[10,79]->PD[X[6,2,7,1],X[8,4,9,3],X[12,6,13,5],X[18,13,19,14],X[16,9,17,10],X[10,17,11,18],X[20,15,1,16],X[14,19,15,20],X[2,8,3,7],X[4,12,5,11]],Knot[10,80]->PD[X[1,4,2,5],X[3,8,4,9],X[5,12,6,13],X[13,18,14,19],X[9,16,10,17],X[17,10,18,11],X[15,20,16,1],X[19,14,20,15],X[11,6,12,7],X[7,2,8,3]],Knot[10,81]->PD[X[4,2,5,1],X[8,4,9,3],X[12,6,13,5],X[16,9,17,10],X[20,17,1,18],X[18,13,19,14],X[14,19,15,20],X[10,15,11,16],X[6,12,7,11],X[2,8,3,7]],Knot[10,82]->PD[X[1,6,2,7],X[7,16,8,17],X[3,9,4,8],X[15,3,16,2],X[5,15,6,14],X[9,5,10,4],X[11,18,12,19],X[13,20,14,1],X[17,10,18,11],X[19,12,20,13]],Knot[10,83]->PD[X[1,6,2,7],X[5,16,6,17],X[13,1,14,20],X[7,15,8,14],X[3,9,4,8],X[9,5,10,4],X[19,11,20,10],X[11,19,12,18],X[17,13,18,12],X[15,2,16,3]],Knot[10,84]->PD[X[4,2,5,1],X[10,4,11,3],X[8,12,9,11],X[20,15,1,16],X[16,5,17,6],X[12,18,13,17],X[14,8,15,7],X[18,14,19,13],X[6,19,7,20],X[2,10,3,9]],Knot[10,85]->PD[X[6,2,7,1],X[16,6,17,5],X[18,11,19,12],X[14,7,15,8],X[8,3,9,4],X[4,9,5,10],X[20,13,1,14],X[10,17,11,18],X[12,19,13,20],X[2,16,3,15]],Knot[10,86]->PD[X[6,2,7,1],X[16,8,17,7],X[8,3,9,4],X[2,15,3,16],X[14,5,15,6],X[4,9,5,10],X[20,14,1,13],X[10,20,11,19],X[18,12,19,11],X[12,18,13,17]],Knot[10,87]->PD[X[4,2,5,1],X[10,4,11,3],X[14,6,15,5],X[20,16,1,15],X[16,7,17,8],X[6,19,7,20],X[8,12,9,11],X[18,13,19,14],X[12,17,13,18],X[2,10,3,9]],Knot[10,88]->PD[X[4,2,5,1],X[20,14,1,13],X[8,3,9,4],X[2,9,3,10],X[14,7,15,8],X[18,15,19,16],X[12,6,13,5],X[10,18,11,17],X[16,12,17,11],X[6,19,7,20]],Knot[10,89]->PD[X[4,2,5,1],X[12,8,13,7],X[8,3,9,4],X[2,9,3,10],X[20,13,1,14],X[14,5,15,6],X[6,19,7,20],X[18,16,19,15],X[16,11,17,12],X[10,17,11,18]],Knot[10,90]->PD[X[6,2,7,1],X[2,8,3,7],X[18,14,19,13],X[14,5,15,6],X[20,12,1,11],X[12,20,13,19],X[8,15,9,16],X[10,4,11,3],X[16,9,17,10],X[4,17,5,18]],Knot[10,91]->PD[X[6,2,7,1],X[20,6,1,5],X[16,9,17,10],X[10,3,11,4],X[2,18,3,17],X[14,7,15,8],X[8,15,9,16],X[12,20,13,19],X[18,12,19,11],X[4,13,5,14]],Knot[10,92]->PD[X[4,2,5,1],X[10,4,11,3],X[14,6,15,5],X[20,16,1,15],X[16,12,17,11],X[18,7,19,8],X[12,18,13,17],X[6,19,7,20],X[8,14,9,13],X[2,10,3,9]],Knot[10,93]->PD[X[6,2,7,1],X[16,6,17,5],X[20,8,1,7],X[18,13,19,14],X[14,9,15,10],X[10,3,11,4],X[4,11,5,12],X[12,17,13,18],X[8,20,9,19],X[2,16,3,15]],Knot[10,94]->PD[X[6,2,7,1],X[2,8,3,7],X[18,12,19,11],X[14,5,15,6],X[20,14,1,13],X[8,15,9,16],X[10,4,11,3],X[16,9,17,10],X[4,17,5,18],X[12,20,13,19]],Knot[10,95]->PD[X[1,4,2,5],X[3,10,4,11],X[11,17,12,16],X[15,9,16,8],X[19,7,20,6],X[5,15,6,14],X[7,19,8,18],X[13,1,14,20],X[17,13,18,12],X[9,2,10,3]],Knot[10,96]->PD[X[1,4,2,5],X[5,18,6,19],X[3,9,4,8],X[9,3,10,2],X[11,17,12,16],X[7,12,8,13],X[15,6,16,7],X[17,11,18,10],X[13,1,14,20],X[19,15,20,14]],Knot[10,97]->PD[X[4,2,5,1],X[12,6,13,5],X[8,3,9,4],X[2,9,3,10],X[16,12,17,11],X[10,18,11,17],X[18,8,19,7],X[20,14,1,13],X[14,20,15,19],X[6,16,7,15]],Knot[10,98]->PD[X[1,6,2,7],X[3,10,4,11],X[7,18,8,19],X[17,8,18,9],X[9,2,10,3],X[11,16,12,17],X[5,15,6,14],X[15,5,16,4],X[13,20,14,1],X[19,12,20,13]],Knot[10,99]->PD[X[6,2,7,1],X[10,4,11,3],X[16,11,17,12],X[14,7,15,8],X[8,15,9,16],X[20,13,1,14],X[12,19,13,20],X[18,6,19,5],X[2,10,3,9],X[4,18,5,17]],Knot[10,100]->PD[X[6,2,7,1],X[18,6,19,5],X[20,13,1,14],X[14,7,15,8],X[10,3,11,4],X[16,9,17,10],X[4,11,5,12],X[8,15,9,16],X[12,19,13,20],X[2,18,3,17]],Knot[10,101]->PD[X[4,2,5,1],X[10,4,11,3],X[14,6,15,5],X[20,16,1,15],X[16,12,17,11],X[12,20,13,19],X[18,8,19,7],X[6,14,7,13],X[8,18,9,17],X[2,10,3,9]],Knot[10,102]->PD[X[6,2,7,1],X[16,10,17,9],X[10,3,11,4],X[2,15,3,16],X[14,5,15,6],X[18,8,19,7],X[4,11,5,12],X[8,18,9,17],X[20,14,1,13],X[12,20,13,19]],Knot[10,103]->PD[X[6,2,7,1],X[18,6,19,5],X[20,13,1,14],X[16,7,17,8],X[10,3,11,4],X[4,11,5,12],X[14,9,15,10],X[8,15,9,16],X[12,19,13,20],X[2,18,3,17]],Knot[10,104]->PD[X[6,2,7,1],X[16,4,17,3],X[18,9,19,10],X[14,7,15,8],X[20,13,1,14],X[8,17,9,18],X[10,19,11,20],X[12,6,13,5],X[4,12,5,11],X[2,16,3,15]],Knot[10,105]->PD[X[4,2,5,1],X[12,4,13,3],X[20,8,1,7],X[16,5,17,6],X[6,15,7,16],X[10,17,11,18],X[18,9,19,10],X[8,14,9,13],X[14,20,15,19],X[2,12,3,11]],Knot[10,106]->PD[X[6,2,7,1],X[16,8,17,7],X[10,3,11,4],X[2,15,3,16],X[14,5,15,6],X[4,11,5,12],X[18,10,19,9],X[20,14,1,13],X[8,18,9,17],X[12,20,13,19]],Knot[10,107]->PD[X[1,4,2,5],X[3,12,4,13],X[7,14,8,15],X[9,19,10,18],X[19,7,20,6],X[5,17,6,16],X[17,11,18,10],X[13,8,14,9],X[15,1,16,20],X[11,2,12,3]],Knot[10,108]->PD[X[6,2,7,1],X[16,4,17,3],X[20,13,1,14],X[14,7,15,8],X[8,19,9,20],X[18,9,19,10],X[10,17,11,18],X[12,6,13,5],X[4,12,5,11],X[2,16,3,15]],Knot[10,109]->PD[X[6,2,7,1],X[10,4,11,3],X[18,11,19,12],X[16,7,17,8],X[8,17,9,18],X[20,15,1,16],X[12,19,13,20],X[14,6,15,5],X[2,10,3,9],X[4,14,5,13]],Knot[10,110]->PD[X[1,6,2,7],X[7,20,8,1],X[3,11,4,10],X[5,16,6,17],X[17,8,18,9],X[9,14,10,15],X[11,3,12,2],X[15,4,16,5],X[13,19,14,18],X[19,13,20,12]],Knot[10,111]->PD[X[6,2,7,1],X[10,4,11,3],X[14,8,15,7],X[8,14,9,13],X[2,10,3,9],X[18,12,19,11],X[16,5,17,6],X[4,17,5,18],X[20,16,1,15],X[12,20,13,19]],Knot[10,112]->PD[X[6,2,7,1],X[8,3,9,4],X[18,11,19,12],X[20,13,1,14],X[2,16,3,15],X[4,17,5,18],X[12,19,13,20],X[10,6,11,5],X[14,7,15,8],X[16,10,17,9]],Knot[10,113]->PD[X[4,2,5,1],X[10,4,11,3],X[14,6,15,5],X[20,16,1,15],X[12,7,13,8],X[8,18,9,17],X[6,19,7,20],X[16,12,17,11],X[18,13,19,14],X[2,10,3,9]],Knot[10,114]->PD[X[6,2,7,1],X[8,3,9,4],X[18,13,19,14],X[20,11,1,12],X[12,19,13,20],X[2,16,3,15],X[4,17,5,18],X[10,6,11,5],X[14,7,15,8],X[16,10,17,9]],Knot[10,115]->PD[X[6,2,7,1],X[14,6,15,5],X[20,15,1,16],X[16,7,17,8],X[8,19,9,20],X[18,11,19,12],X[10,4,11,3],X[4,10,5,9],X[12,17,13,18],X[2,14,3,13]],Knot[10,116]->PD[X[6,2,7,1],X[16,3,17,4],X[14,7,15,8],X[8,15,9,16],X[10,18,11,17],X[18,6,19,5],X[20,13,1,14],X[12,19,13,20],X[2,10,3,9],X[4,11,5,12]],Knot[10,117]->PD[X[1,6,2,7],X[5,16,6,17],X[13,1,14,20],X[7,15,8,14],X[19,9,20,8],X[3,11,4,10],X[11,5,12,4],X[9,19,10,18],X[17,13,18,12],X[15,2,16,3]],Knot[10,118]->PD[X[6,2,7,1],X[18,6,19,5],X[20,13,1,14],X[12,19,13,20],X[14,7,15,8],X[8,3,9,4],X[2,16,3,15],X[10,18,11,17],X[16,10,17,9],X[4,11,5,12]],Knot[10,119]->PD[X[1,6,2,7],X[7,18,8,19],X[3,9,4,8],X[17,3,18,2],X[5,15,6,14],X[9,17,10,16],X[15,11,16,10],X[11,5,12,4],X[13,20,14,1],X[19,12,20,13]],Knot[10,120]->PD[X[1,6,2,7],X[5,18,6,19],X[13,20,14,1],X[11,16,12,17],X[3,10,4,11],X[7,12,8,13],X[9,4,10,5],X[15,8,16,9],X[19,14,20,15],X[17,2,18,3]],Knot[10,121]->PD[X[1,6,2,7],X[7,20,8,1],X[9,19,10,18],X[3,11,4,10],X[17,5,18,4],X[5,12,6,13],X[11,16,12,17],X[19,14,20,15],X[13,8,14,9],X[15,2,16,3]],Knot[10,122]->PD[X[1,6,2,7],X[7,15,8,14],X[15,2,16,3],X[5,12,6,13],X[9,19,10,18],X[3,11,4,10],X[17,5,18,4],X[19,9,20,8],X[11,16,12,17],X[13,1,14,20]],Knot[10,123]->PD[X[8,2,9,1],X[10,3,11,4],X[12,6,13,5],X[4,18,5,17],X[18,11,19,12],X[2,15,3,16],X[16,10,17,9],X[20,14,1,13],X[14,7,15,8],X[6,19,7,20]],Knot[10,124]->PD[X[4,2,5,1],X[8,4,9,3],X[9,17,10,16],X[5,15,6,14],X[15,7,16,6],X[11,19,12,18],X[13,1,14,20],X[17,11,18,10],X[19,13,20,12],X[2,8,3,7]],Knot[10,125]->PD[X[1,4,2,5],X[3,8,4,9],X[5,14,6,15],X[20,16,1,15],X[16,10,17,9],X[18,12,19,11],X[10,18,11,17],X[12,20,13,19],X[13,6,14,7],X[7,2,8,3]],Knot[10,126]->PD[X[4,2,5,1],X[8,4,9,3],X[5,14,6,15],X[15,20,16,1],X[9,16,10,17],X[11,18,12,19],X[17,10,18,11],X[19,12,20,13],X[13,6,14,7],X[2,8,3,7]],Knot[10,127]->PD[X[1,4,2,5],X[3,8,4,9],X[14,6,15,5],X[15,20,16,1],X[9,16,10,17],X[11,18,12,19],X[17,10,18,11],X[19,12,20,13],X[6,14,7,13],X[7,2,8,3]],Knot[10,128]->PD[X[4,2,5,1],X[8,4,9,3],X[9,17,10,16],X[5,15,6,14],X[15,7,16,6],X[13,1,14,20],X[19,11,20,10],X[11,19,12,18],X[17,13,18,12],X[2,8,3,7]],Knot[10,129]->PD[X[1,4,2,5],X[3,8,4,9],X[5,14,6,15],X[20,16,1,15],X[16,10,17,9],X[10,20,11,19],X[18,12,19,11],X[12,18,13,17],X[13,6,14,7],X[7,2,8,3]],Knot[10,130]->PD[X[4,2,5,1],X[8,4,9,3],X[5,14,6,15],X[15,20,16,1],X[9,16,10,17],X[19,10,20,11],X[11,18,12,19],X[17,12,18,13],X[13,6,14,7],X[2,8,3,7]],Knot[10,131]->PD[X[1,4,2,5],X[3,8,4,9],X[14,6,15,5],X[15,20,16,1],X[9,16,10,17],X[19,10,20,11],X[11,18,12,19],X[17,12,18,13],X[6,14,7,13],X[7,2,8,3]],Knot[10,132]->PD[X[4,2,5,1],X[8,4,9,3],X[5,12,6,13],X[15,18,16,19],X[9,16,10,17],X[17,10,18,11],X[13,20,14,1],X[19,14,20,15],X[11,6,12,7],X[2,8,3,7]],Knot[10,133]->PD[X[1,4,2,5],X[3,8,4,9],X[14,9,15,10],X[5,13,6,12],X[13,7,14,6],X[18,11,19,12],X[20,15,1,16],X[16,19,17,20],X[10,17,11,18],X[7,2,8,3]],Knot[10,134]->PD[X[4,2,5,1],X[8,4,9,3],X[9,15,10,14],X[5,13,6,12],X[13,7,14,6],X[11,19,12,18],X[15,1,16,20],X[19,17,20,16],X[17,11,18,10],X[2,8,3,7]],Knot[10,135]->PD[X[1,4,2,5],X[3,8,4,9],X[9,15,10,14],X[12,5,13,6],X[6,13,7,14],X[11,19,12,18],X[15,1,16,20],X[19,17,20,16],X[17,11,18,10],X[7,2,8,3]],Knot[10,136]->PD[X[1,4,2,5],X[5,10,6,11],X[3,9,4,8],X[9,3,10,2],X[14,8,15,7],X[18,12,19,11],X[20,15,1,16],X[16,19,17,20],X[12,18,13,17],X[6,14,7,13]],Knot[10,137]->PD[X[1,4,2,5],X[5,10,6,11],X[3,9,4,8],X[9,3,10,2],X[16,12,17,11],X[14,7,15,8],X[6,15,7,16],X[20,18,1,17],X[18,13,19,14],X[12,19,13,20]],Knot[10,138]->PD[X[4,2,5,1],X[10,6,11,5],X[8,3,9,4],X[2,9,3,10],X[16,12,17,11],X[7,15,8,14],X[15,7,16,6],X[20,18,1,17],X[18,13,19,14],X[12,19,13,20]],Knot[10,139]->PD[X[4,2,5,1],X[10,4,11,3],X[11,19,12,18],X[5,15,6,14],X[7,17,8,16],X[15,7,16,6],X[17,9,18,8],X[13,1,14,20],X[19,13,20,12],X[2,10,3,9]],Knot[10,140]->PD[X[1,4,2,5],X[3,10,4,11],X[11,19,12,18],X[14,5,15,6],X[6,17,7,18],X[16,7,17,8],X[8,15,9,16],X[13,1,14,20],X[19,13,20,12],X[9,2,10,3]],Knot[10,141]->PD[X[1,4,2,5],X[3,10,4,11],X[14,6,15,5],X[16,8,17,7],X[6,16,7,15],X[17,20,18,1],X[11,18,12,19],X[19,12,20,13],X[8,14,9,13],X[9,2,10,3]],Knot[10,142]->PD[X[4,2,5,1],X[10,4,11,3],X[11,19,12,18],X[5,15,6,14],X[17,7,18,6],X[7,17,8,16],X[15,9,16,8],X[13,1,14,20],X[19,13,20,12],X[2,10,3,9]],Knot[10,143]->PD[X[4,2,5,1],X[10,4,11,3],X[5,14,6,15],X[7,16,8,17],X[15,6,16,7],X[17,20,18,1],X[11,18,12,19],X[19,12,20,13],X[13,8,14,9],X[2,10,3,9]],Knot[10,144]->PD[X[1,4,2,5],X[3,10,4,11],X[18,11,19,12],X[5,15,6,14],X[17,7,18,6],X[7,17,8,16],X[15,9,16,8],X[20,13,1,14],X[12,19,13,20],X[9,2,10,3]],Knot[10,145]->PD[X[4,2,5,1],X[5,12,6,13],X[8,3,9,4],X[2,9,3,10],X[11,16,12,17],X[17,10,18,11],X[7,18,8,19],X[13,20,14,1],X[19,14,20,15],X[15,6,16,7]],Knot[10,146]->PD[X[4,2,5,1],X[5,18,6,19],X[8,3,9,4],X[2,9,3,10],X[11,17,12,16],X[7,12,8,13],X[15,6,16,7],X[17,11,18,10],X[13,1,14,20],X[19,15,20,14]],Knot[10,147]->PD[X[4,2,5,1],X[10,4,11,3],X[5,14,6,15],X[15,20,16,1],X[12,7,13,8],X[8,18,9,17],X[19,7,20,6],X[16,12,17,11],X[18,13,19,14],X[2,10,3,9]],Knot[10,148]->PD[X[4,2,5,1],X[8,4,9,3],X[5,12,6,13],X[13,18,14,19],X[9,16,10,17],X[17,10,18,11],X[15,20,16,1],X[19,14,20,15],X[11,6,12,7],X[2,8,3,7]],Knot[10,149]->PD[X[1,4,2,5],X[3,8,4,9],X[12,6,13,5],X[13,18,14,19],X[9,16,10,17],X[17,10,18,11],X[15,20,16,1],X[19,14,20,15],X[6,12,7,11],X[7,2,8,3]],Knot[10,150]->PD[X[4,2,5,1],X[8,4,9,3],X[5,12,6,13],X[9,17,10,16],X[17,1,18,20],X[13,19,14,18],X[19,15,20,14],X[15,11,16,10],X[11,6,12,7],X[2,8,3,7]],Knot[10,151]->PD[X[1,4,2,5],X[3,8,4,9],X[12,6,13,5],X[9,17,10,16],X[17,1,18,20],X[13,19,14,18],X[19,15,20,14],X[15,11,16,10],X[6,12,7,11],X[7,2,8,3]],Knot[10,152]->PD[X[1,6,2,7],X[3,8,4,9],X[5,12,6,13],X[18,13,19,14],X[16,9,17,10],X[10,17,11,18],X[20,15,1,16],X[14,19,15,20],X[7,2,8,3],X[11,4,12,5]],Knot[10,153]->PD[X[4,2,5,1],X[8,4,9,3],X[12,6,13,5],X[13,18,14,19],X[9,16,10,17],X[17,10,18,11],X[15,20,16,1],X[19,14,20,15],X[6,12,7,11],X[2,8,3,7]],Knot[10,154]->PD[X[4,2,5,1],X[8,4,9,3],X[12,6,13,5],X[9,17,10,16],X[17,1,18,20],X[13,19,14,18],X[19,15,20,14],X[15,11,16,10],X[6,12,7,11],X[2,8,3,7]],Knot[10,155]->PD[X[1,6,2,7],X[7,16,8,17],X[3,11,4,10],X[15,3,16,2],X[5,15,6,14],X[11,5,12,4],X[9,18,10,19],X[20,14,1,13],X[17,8,18,9],X[12,20,13,19]],Knot[10,156]->PD[X[4,2,5,1],X[12,4,13,3],X[7,14,8,15],X[18,9,19,10],X[6,19,7,20],X[16,5,17,6],X[10,17,11,18],X[13,8,14,9],X[20,15,1,16],X[2,12,3,11]],Knot[10,157]->PD[X[1,6,2,7],X[10,4,11,3],X[16,11,17,12],X[7,15,8,14],X[15,9,16,8],X[13,1,14,20],X[19,13,20,12],X[18,6,19,5],X[2,10,3,9],X[4,18,5,17]],Knot[10,158]->PD[X[6,2,7,1],X[3,10,4,11],X[14,8,15,7],X[8,14,9,13],X[9,2,10,3],X[11,18,12,19],X[5,17,6,16],X[17,5,18,4],X[20,16,1,15],X[19,12,20,13]],Knot[10,159]->PD[X[1,6,2,7],X[3,9,4,8],X[18,11,19,12],X[20,13,1,14],X[15,2,16,3],X[17,5,18,4],X[12,19,13,20],X[5,10,6,11],X[7,15,8,14],X[9,16,10,17]],Knot[10,160]->PD[X[4,2,5,1],X[12,4,13,3],X[7,14,8,15],X[9,19,10,18],X[19,7,20,6],X[5,17,6,16],X[17,11,18,10],X[13,8,14,9],X[15,1,16,20],X[2,12,3,11]],Knot[10,161]->PD[X[1,4,2,5],X[3,12,4,13],X[7,14,8,15],X[18,9,19,10],X[6,19,7,20],X[16,5,17,6],X[10,17,11,18],X[13,8,14,9],X[20,15,1,16],X[11,2,12,3]],Knot[10,162]->PD[X[6,2,7,1],X[16,10,17,9],X[10,3,11,4],X[2,15,3,16],X[14,5,15,6],X[18,8,19,7],X[4,11,5,12],X[8,18,9,17],X[13,20,14,1],X[19,12,20,13]],Knot[10,163]->PD[X[6,2,7,1],X[8,3,9,4],X[13,19,14,18],X[11,1,12,20],X[19,13,20,12],X[2,16,3,15],X[4,17,5,18],X[10,6,11,5],X[14,7,15,8],X[16,10,17,9]],Knot[10,164]->PD[X[6,2,7,1],X[14,7,15,8],X[15,2,16,3],X[5,12,6,13],X[9,19,10,18],X[3,11,4,10],X[17,5,18,4],X[19,9,20,8],X[11,16,12,17],X[20,13,1,14]],Knot[10,165]->PD[X[1,6,2,7],X[7,18,8,19],X[3,9,4,8],X[17,3,18,2],X[5,15,6,14],X[9,17,10,16],X[15,11,16,10],X[11,5,12,4],X[20,14,1,13],X[12,20,13,19]],GST48->PD[X[1,15,2,14],X[29,2,30,3],X[40,4,41,3],X[4,44,5,43],X[5,26,6,27],X[95,7,96,6],X[7,1,8,96],X[8,14,9,13],X[28,9,29,10],X[41,11,42,10],X[11,43,12,42],X[12,27,13,28],X[15,31,16,30],X[61,16,62,17],X[72,17,73,18],X[83,18,84,19],X[34,20,35,19],X[20,89,21,90],X[92,21,93,22],X[22,79,23,80],X[23,68,24,69],X[24,57,25,58],X[56,25,57,26],X[31,63,32,62],X[32,74,33,73],X[33,85,34,84],X[35,50,36,51],X[81,37,82,36],X[70,38,71,37],X[59,39,60,38],X[54,39,55,40],X[55,45,56,44],X[45,59,46,58],X[46,70,47,69],X[47,81,48,80],X[91,49,92,48],X[49,91,50,90],X[82,52,83,51],X[71,53,72,52],X[60,54,61,53],X[74,63,75,64],X[85,64,86,65],X[65,76,66,77],X[66,87,67,88],X[94,67,95,68],X[86,75,87,76],X[77,88,78,89],X[93,78,94,79]]};

Our blackboard from September 16:

KB[pd_PD] := Module[{p,t1,t2,t3,t4,B,d},
SetAttributes[p,Orderless];
t1=pd/. X[i_,j_,k_,l_]->A*p[i,j]*p[k,l]+B*p[i,l]p[j,k];
t2=Expand[t1 /. PD->Times];
t3=t2 //. {p[i_,j_]p[j_,k_]->p[i,k]};
t4=t3 /. {p[i_,i_]->d, p[i_,j_]^2 ->d};
Expand[t4/.{B->1/A, d->-A^2-1/A^2}]
]

Knots

Knot[8,17]/.Knots

KB[Knot[8,17]/.Knots]

tab10=Table[
Echo[Timing[{k,KB[Knot[10,k]/.Knots]}]],
{k,165}
]

Expand[(a+b)^2]

Expand[(a+b)^2] // TreeForm

tab10[[1;;3]] // TreeForm

f[1,2,3]

f[1,2,3]//TreeForm

g@@f[1,2,3]

Plus@@{1,2,3}

Plus@@tab10

165 166/2

KB[GST48/.Knots]

KB[pd_PD] := Module[{p,t1,t2,t3,t4,B,d},
SetAttributes[p,Orderless];
t1=pd/. X[i_,j_,k_,l_]->A*p[i,j]*p[k,l]+B*p[i,l]p[j,k];
t2=Expand[t1 /. PD->Times];
t3=t2 //. {p[i_,j_]p[j_,k_]->p[i,k]};
t4=t3 /. {p[i_,i_]->d, p[i_,j_]^2 ->d};
Expand[t4/.{B->1/A, d->-A^2-1/A^2}]
]

Times@@{1,2,3,4,5,6,7}

Times@@{}

pd=GST48/.Knots

First[pd]

Last[pd]

DeleteCases[{1,2,3},2]

FKB[pd_PD] := Module[{p,t1,t2,t3,t4,B,d,KB,todo},
SetAttributes[p,Orderless];
KB=1;
todo=pd;
While[Length[todo]>0,
x=First[todo];
todo=DeleteCases[todo,x];
t1=KB(x/. X[i_,j_,k_,l_]->A*p[i,j]*p[k,l]+B*p[i,l]*p[j,k]);
t2=Expand[t1];
t3=t2 //. {p[i_,j_]p[j_,k_]->p[i,k]};
t4=t3 /. {p[i_,i_]->d, p[i_,j_]^2 ->d};
KB=Expand[t4/.{B->1/A, d->-A^2-1/A^2}];
];
KB
]

FKB[Knot[8,17]/.Knots]

Timing[Table[FKB[Knot[10,k]/.Knots], {k,165}];]

Table[CatalanNumber[k],{k,1,20}]

{1,2,3}⋃{3,4}

{1,2,3}⋂{3,4}

Complement[{1,2,3,4},{3}]

x

List@@x

front={1,2,3,6,9,10,11}

todo=List@@PD[X[1,2,5,12],X[1,2,3,13]]

v[x_X]:=Length[front⋂(List@@x)]

v/@todo

MaximalBy[todo,v]

pd

RandomChoice[List@@pd]

EFKB[pd_PD] := Module[{p,t1,t2,t3,t4,B,d,KB,todo,front,x,v},
SetAttributes[p,Orderless];
KB=1;
todo=List@@pd;
front={};
v[x_X]:=Length[front⋂(List@@x)];
While[Length[todo]>0,
x=RandomChoice[MaximalBy[todo,v]];
todo=DeleteCases[todo,x];
t1=KB(x/. X[i_,j_,k_,l_]->A*p[i,j]*p[k,l]+B*p[i,l]*p[j,k]);
t2=Expand[t1];
t3=t2 //. {p[i_,j_]p[j_,k_]->p[i,k]};
t4=t3 /. {p[i_,i_]->d, p[i_,j_]^2 ->d};
KB=Expand[t4/.{B->1/A, d->-A^2-1/A^2}];
front=Complement[front⋃(List@@x), front⋂(List@@x)];
];
KB
]

Timing[Table[EFKB[Knot[10,k]/.Knots], {k,165}];]

Table[EFKB[Knot[10,k]/.Knots]==FKB[Knot[10,k]/.Knots], {k,165}]

Timing[EFKB[GST48/.Knots]]

Blackboard at end: